Fundamental Structural Analysis by W. J. Spencer
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Fundamental Structural Analysis by W. J. Spencer

PREFACE to Fundamental Structural Analysis by W. J. Spencer

Significant changes have occurred in the approach to structural analysis over the last twenty years. These changes have been brought about by a more general understanding of the nature of the problem and the development of the digital computer.

Almost all s~ructural engineering offices throughout the world would now have access to some form of digital computer, ranging from hand-held programmable calculators through to the largest machines available.

Powerful microcomputers are also widely available and many engineers and students have personal computers as a general aid to their work.

Problems in structural analysis have now been formulated in such a way that the solution is available through the use of the computer, largely by what is known as matrix methods of structural analysis.

It is interesting to note that such methods do not put forward new theories in structural analysis, rather they are a restatement of classical theory in a manner that can be directly related to the computer.

This book begins with the premise that most structural analysis will be done on a computer. This is not to say that a fundamental understanding of structural behaviour is not presented or that only computer-based techniques are given.

Indeed, the reverse is true. Understanding structural behaviour is an underlying theme and many solution techniques suitable for hand computation, such as moment distribution, are retained.

The most widely used method of computer-based structural analysis is the matrix stiffness method. For this reason, all of the fundamental concepts of structures and structural behaviour are presented against the background of the matrix stiffness method.

The result is that the student is naturally introduced to the use of the computer in structural analysis, and neither matrix methods nor the computer are treated as an addendum.

Matrix algebra is now well taught in undergraduate mathematics courses and it is assumed that the reader is well acquainted with the subject.

In many instances the solution techniques require the manipulation of matrices and the solution of systems of simultaneous linear equations.

These are the operations that the digital computer can most readily handle and they are operations which are built into computer application programs in structural engineering.

For the student, however, it is important that these operations are understood, so that it is desirable to have a form of matrix manipulation computer program available.

Many programmable pocket calculators currently provide for such operations and there is no doubt that the capacity and speed with which these machines can carry out these tasks will increase with further developments.

Some computer languages, notably some versions of BASIC, provide for general matrix manipulation, and scientific library subroutines for handling matrices are provided with other languages such as Fortran.

A third possibility is to provide a computer program in the form of a problem-orientated language, with a command structure directly aimed at facilitating the manipulation of matrices.

Such a computer program, known as MATOP and developed by the author, is presented as an appendix to the text and used with illustrative examples throughout.

The program is not unique and other such programs have been widely available for a number of years. The text is seen as a first course in structural mechanics or the theory of structures.

Although it is assumed that students will have done a first course in the more general field of applied mechanics including simple beam theory and stress analysis.

The material is probably more than can be covered in two semesters, and indeed it has been delivered over three semesters.

The first two chapters outline the fundamental principles and introduce students to the nature of structures and the structural analysis problem.

A detailed study of equilibrium and statical and kinematic determinacy is presented in chapter 2. In chapter 3, the foundations of the matrix stiffness method are presented and the ideas of element and structure stiffness matrices are developed.

The classical slope-deflection equations are developed from simple beam theory in this chapter, and presented in matrix notation to give the general beam element stiffness matrix.

The matrix stiffness method is further developed in chapter 4, where it is applied to continuous beams and rectangular frames.

At this stage coordinate transformation is not introduced and axial deformation of the element is ignored. The approach leads to some powerful applications where the analysis results can be obtained quite rapidly, particularly with the use of the direct stiffness method.

It is shown in many instances that the solution is reduced to one of handling matrices of a size that can be adequately dealt with on a pocket calculator.

The moment distribution method has been retained as a useful hand method of analysis and this is detailed in chapter 5, with applications to beams and rectangular frames.

The work is closely related to that of chapter 4 and the moment distribution method is shown as a logical variation of the matrix stiffness method.

Chapter 6 returns to the matrix stiffness method to introduce the general stiffness method and coordinate transformation. A wider range of structures is now considered, including composite structures where elements of different types are introduced into the one structure.

A fundamental study of structural analysis must include a reference to the principle of virtual work which is presented in chapter 7.

Both the principle of virtual displacements and the principle of virtual forces are considered. The principle of virtual forces, particularly with regard to expressions for the deflection of structures, leads logically into the flexibility method of analysis presented in chapter 8.

This provides an alternative approach to the stiffness method and gives a balance to the overall study. The author is convinced that the general use of computer programs for structural analysis makes demands for greater, rather than less, awareness and understanding of structural behaviour on the part of users.

Structural computations must still be checked, results must still be interpreted and engineering judgement must still be exercised.

To facilitate this, a chapter on approximate methods of analysis is included (chapter 9). It is presented at this stage since it is felt that approximate methods can only be introduced against a background of general knowledge of structural behaviour.

In a final chapter, some general guidance to computer application programs in structural analysis is presented. Some aspects of modelling of structures are also discussed.

Numerous examples are given throughout the text and a common thread is achieved through the use of the program MATOP, details of which are given in an appendix with a program listing in Fortran 77.

Much of the data presented throughout the text is collected together in another appendix as a 'Structural Mechanics Students' Handbook'.

The significant data here is a collective statement of the element stiffness matrices for various element types.

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